Dimensions panel: how to proportionaly get all 3 dimensions entering just one
It's where still the Scale operation should be used. The question is how to obtain right factor for scaling.
The brute force method is to calculate how many times is 2.5 less than 3.356:

3.356 / 2.5 = 1.342

So you want the object to become 1.342 times smaller.
Press S for Scale operation. But if entering 1.342 right now, it will scale 1.342 times bigger, not smaller. 

So the only step is to invert this. In order to avoid any 3-rd party calculations, after pressing S enter "=" sign (no quotes) which will make Blender to treat further text as formula and then 1 / 1.342. The final formula:

Press S, then = 1 / 1.342.

This method is brute force at least because final Y dimension would be 2.501 (with mentioned values). This should have to do with floating point precision.